Finding the least value

[Yellybean]

Hello,

Find the least interval <a;b> in which are all (x;y;z) solutions of this equation:
15(x+y+z) = 12(xy+xz+yz) = 10(x^2 + y^2 + z^2)

I have no idea how to count that. I just proved that (x+y+z) = 4 but what else may i calculate?

Thank you. Jellybean

 

[Yellybean]

I solved it already, so np
Just wanted to say you, the only solution isnt permutation of (1;1;2) but for example 2/3 5/3 5/3. But never mind, thank you for answer